Constant potentials in 6D Einstein-Gauss-Bonnet theory

The qualitative physical behavior of six-dimensional perfect fluid spheres is studied in the context of Einstein-Gauss-Bonnet (EGB) gravity theory, and a contrast is drawn with the associated Einstein model. At first we seek an analogue of the defective Einstein universe by setting the temporal potential to be constant. The equation of state ρ + 53 p = a constant multiple of the Gauss-Bonnet coupling α is obtained, and in the case of vanishing α the six-dimensional Einstein universe is recovered. More significantly the case of a constant spatial potential generated an exact solution in terms of hypergeometric functions. No solution in terms of elementary functions was located; however it was still possible to construct a compact star with finite radius for a specific choice of potential and suitable parameter values obtained by fine-tuning. It emerged that the EGB model was singularity free and displayed a number of pleasing physical features which were extrapolated from the usual restrictions placed on Einstein spheres. It was found that the EGB higher curvature terms allowed for the existence of stellar radius some 20 times larger than its Einstein counterpart. Moreover, the Einstein model suffered the permanent defect of a central singularity. In many respects the Gauss-Bonnet offered corrections to the corresponding Einstein model.